A note on the approximation of Dirichlet boundary control problems for the wave equation on curved domains

References

• Casas , E and Sokolowski , J . 2010 . Approximation of boundary control problems on curved domains . SIAM J. Control Opt. , 48 : 3746 – 3780 .
   Web of Science ®Google Scholar
• Casas , E and Raymond , J-P . 2006 . Error estimates for the numerical approximation of Dirichlet boundary control for semilinear elliptic equations . SIAM J. Control Optim. , 45 : 1586 – 1611 .
   Web of Science ®Google Scholar
• Deckelnick , K , Guenther , A and Hinze , M . 2009 . Finite element approximation of Dirichlet boundary control for elliptic PDEs on two and three-dimensional curved domains . SIAM J. Control Optim. , 48 : 2798 – 2819 .
   Google Scholar
• Tröltzsch , F . 2010 . Optimal Control of Partial Differential Equations , Providence, RI : American Mathematical Society .
   Google Scholar
• Kowalewski , A , Lasiecka , I and Sokolowski , J . 2012 . Sensitivity analysis of hyperbolic optimal control problems . Comput. Optim. Appl. , 52 : 147 – 179 .
   Web of Science ®Google Scholar
• Lax , P . 2006 . Hyperbolic Partial Differential Equations, Courant Lecture Notes in Mathematics , Providence, RI : American Mathematical Society .
   Google Scholar
• Grisvard , P . 1989 . Controllabilite exacte des solutions de l'equation des ondes en presence de singularites . J. Math. Pures Appl. , 68 : 215 – 259 .
   Web of Science ®Google Scholar
• Bramble , J and King , J . 1994 . A robust finite element method for nonhomogeneous Dirichlet problems in domains with curved boundaries . Math. Comput. , 63 : 1 – 17 .
   Web of Science ®Google Scholar
• Gugat , M . 1999 . Time-parametric control: Uniform convergence of the optimal value functions of the discretized problems . Control Cybern. , 28 : 7 – 33 .
   Web of Science ®Google Scholar
• Gugat , M . 2009 . Penalty techniques for state constrained optimal control problems with the wave equation . SIAM J. Control Optim. , 48 : 3026 – 3051 .
   Web of Science ®Google Scholar
• Gugat , M and Grimm , V . 2011 . Optimal boundary control of the wave equation with pointwise control constraints . Comput. Optim. Appl. , 49 : 123 – 147 .
   Web of Science ®Google Scholar
• Bardos , C , Lebeau , G and Rauch , J . 1992 . Sharp sufficient conditions for the observation, control and stabilization of waves from the boundary . SIAM J. Control Optim. , 30 : 1024 – 1065 .
   Web of Science ®Google Scholar
• Lasiecka , I and Triggiani , R . 2000 . Control Theory for Partial Differential Equations: Continuous and Approximation Theories, II Abstract Hyperbolic like Systems over a Finite Time Horizon , Cambridge : Cambridge University Press .
   Google Scholar
• Adams , R and Fournier , JJF . 2003 . Sobolev Spaces , Amsterdam : Academic Press .
   Google Scholar
• Lagnese , J . 1978 . Exact boundary value controllability of a class of hyperbolic equations . SIAM J. Control Optim. , 16 : 1000 – 1017 .
   Web of Science ®Google Scholar
• Ciarlet , PG . 1988 . Mathematical Elasticity, Volume I: Three-Dimensional Elasticity , Amsterdam : North-Holland .
   Google Scholar